TY - JOUR

T1 - The initial development of a jet caused by fluid, body and free surface interaction. Part 4. the large-time structure

AU - Needham, D.J.

N1 - Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012/6/1

Y1 - 2012/6/1

N2 - The free surface and flow field structure generated by the uniform acceleration of a rigid plate, inclined at an angle α ∈ (0, π) to the exterior horizontal, as it advances into an initially stationary and horizontal strip of inviscid incompressible fluid, is studied in the large-time limit via the method of matched asymptotic expansions. The small-time limit of the solution to this problem has been studied in detail in Needham et al. (2008, The initial development of a jet caused by fluid, body and free-surface interaction. Part 3. An inclined accelerating plate. Q. Jl. Mech. Appl. Math., 64, 581-615). We assume that after an initial constant acceleration, the velocity of the plate reaches a terminal value in finite time and remains at that velocity thereafter. The structure of the large-time solution includes a steady bore propagating away from the plate with constant speed, together with an algebraically decaying wave field behind the bore, up to the plate, which demonstrates that there are no localized trapped waves excited near to the plate, with all energy radiating away from the plate as t → ∞.

AB - The free surface and flow field structure generated by the uniform acceleration of a rigid plate, inclined at an angle α ∈ (0, π) to the exterior horizontal, as it advances into an initially stationary and horizontal strip of inviscid incompressible fluid, is studied in the large-time limit via the method of matched asymptotic expansions. The small-time limit of the solution to this problem has been studied in detail in Needham et al. (2008, The initial development of a jet caused by fluid, body and free-surface interaction. Part 3. An inclined accelerating plate. Q. Jl. Mech. Appl. Math., 64, 581-615). We assume that after an initial constant acceleration, the velocity of the plate reaches a terminal value in finite time and remains at that velocity thereafter. The structure of the large-time solution includes a steady bore propagating away from the plate with constant speed, together with an algebraically decaying wave field behind the bore, up to the plate, which demonstrates that there are no localized trapped waves excited near to the plate, with all energy radiating away from the plate as t → ∞.

UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84864766638&md5=c93e45ed97cacaafcb4788bfe488caa1

U2 - 10.1093/imamat/hxr028

DO - 10.1093/imamat/hxr028

M3 - Article

AN - SCOPUS:84864766638

SN - 0272-4960

VL - 77

SP - 451

EP - 472

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 4

ER -